Recent development of trilayer graphene nanoribbon Schottky-barrier field-effect transistors (FETs) will be governed by transistor electrostatics and quantum effects that impose scaling limits like those of Si metal-oxide-semiconductor field-effect transistors. The current–voltage characteristic of a Schottky-barrier FET has been studied as a function of physical parameters such as effective mass, graphene nanoribbon length, gate insulator thickness, and electrical parameters such as Schottky barrier height and applied bias voltage. In this paper, the scaling behaviors of a Schottky-barrier FET using trilayer graphene nanoribbon are studied and analytically modeled. A novel analytical method is also presented for describing a switch in a Schottky-contact double-gate trilayer graphene nanoribbon FET. In the proposed model, different stacking arrangements of trilayer graphene nanoribbon are assumed as metal and semiconductor contacts to form a Schottky transistor. Based on this assumption, an analytical model and numerical solution of the junction current–voltage are presented in which the applied bias voltage and channel length dependence characteristics are highlighted. The model is then compared with other types of transistors. The developed model can assist in comprehending experiments involving graphene nanoribbon Schottky-barrier FETs. It is demonstrated that the proposed structure exhibits negligible short-channel effects, an improved on-current, realistic threshold voltage, and opposite subthreshold slope and meets the International Technology Roadmap for Semiconductors near-term guidelines. Finally, the results showed that there is a fast transient between on-off states. In other words, the suggested model can be used as a high-speed switch where the value of subthreshold slope is small and thus leads to less power consumption.